Planar Projections of Graphs

Aravind, N. R. and Maniyar, Udit (2020) Planar Projections of Graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12016. pp. 453-462. ISSN 0302-9743

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Abstract

We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on n vertices has a representation in \sqrt{n/2}+1 \rceil planes. In 3 dimensions, we show that there exist graphs with edges that can be projected onto two orthogonal planes, and that this is best possible. Finally, we obtain bounds in terms of parameters such as geometric thickness and linear arboricity. Using such a bound, we show that every graph of maximum degree 5 has a plane-projectable representation in 3 dimensions.

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